A042010 - OEIS

%I #13 Sep 08 2022 08:44:55

%S 22,23,1034,1057,47542,48599,2185898,2234497,100503766,102738263,

%T 4620987338,4723725601,212464913782,217188639383,9768765046634,

%U 9985953686017,449150727231382,459136680917399

%N Numerators of continued fraction convergents to sqrt(528).

%H Vincenzo Librandi, <a href="/A042010/b042010.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,46,0,-1).

%F G.f.: -(x^3-22*x^2-23*x-22)/(x^4-46*x^2+1). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 46*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 13 2013

%t Numerator[Convergents[Sqrt[528], 30]] (* or *) CoefficientList[Series[-(x^3 - 22 x^2 - 23 x - 22)/(x^4 - 46 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 13 2013 *)

%o (Magma) I:=[22, 23, 1034, 1057]; [n le 4 select I[n] else 46*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 13 2013

%Y Cf. A042011.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.